Find Out Projection Matrix for Oblique Projection

To find out projection matrix for oblique projection, we want to find out the direction vector d. Because vector PP' and vector d both contain the same direction. Hence, PP'=d 

 So, x'- 0=d₁= f.cosθ

       y'- 0=d₂= f.sinθ

       z'-1=d₃

 Since z'=0 on the xy-plane, d₃ = -1, 

Because, Oblique projection is a particular case of parallel projection, hence, we can transform the common transformation of parallel projection for Oblique projection as given:

Here, f=foreshortening factor, that is the projected length of the z-axis unit vector. When β is the angle among the Oblique projectors and the plane of projection so,

1/f=tan (β) , that is f= cot(β)

θ=angle among the projected line along with the positive x-axis.